A 17-foot ladder is resting against a wall of a building in such a way that the top of the ladder is 14 feet above the ground. How far is the foot of the ladder from the base of the building?

Step 1 ：We are given a right triangle problem where the ladder is the hypotenuse, the height from the ground to the top of the ladder is one side, and the distance from the foot of the ladder to the base of the building is the other side.

Step 2 ：We can use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

Step 3 ：In this case, we know the length of the hypotenuse (17 feet) and one side (14 feet), and we need to find the length of the other side (the distance from the foot of the ladder to the base of the building).

Step 4 ：Let's denote the hypotenuse as \(c\), one side as \(a\), and the other side as \(b\). So, \(c = 17\), \(a = 14\), and we need to find \(b\).

Step 5 ：According to the Pythagorean theorem, \(c^2 = a^2 + b^2\). So, \(b = \sqrt{c^2 - a^2}\).

Step 6 ：Substituting the given values, we get \(b = \sqrt{17^2 - 14^2} = 9.643650760992955\).

Step 7 ：Final Answer: The foot of the ladder is approximately \(\boxed{9.64}\) feet from the base of the building.